Problem: What number could replace $a$ below? $\dfrac{3}{4} = \dfrac{a}{8}$
The fraction on the left represents 3 out of 4 slices of a rectangular cake. What if we cut the cake into 8 slices instead? How many slices would result in the same amount of cake? We would need 6 slices. $\dfrac{3}{4} = \dfrac{6}{8}$ and so the answer is $6$ Another way to get the answer is to multiply by $\dfrac{2}{2}$ $\dfrac{2}{2} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{3}{4} \times \dfrac{2}{2} = \dfrac{6}{8} $ so our answer is $6$.